Theorem nmhmrcl1

Description: Reverse closure for a normed module homomorphism. (Contributed by Mario Carneiro, 18-Oct-2015)

	Ref	Expression
Assertion	nmhmrcl1	|- ( F e. ( S NMHom T ) -> S e. NrmMod )

Proof

Step	Hyp	Ref	Expression
1		isnmhm	|- ( F e. ( S NMHom T ) <-> ( ( S e. NrmMod /\ T e. NrmMod ) /\ ( F e. ( S LMHom T ) /\ F e. ( S NGHom T ) ) ) )
2	1	simplbi	|- ( F e. ( S NMHom T ) -> ( S e. NrmMod /\ T e. NrmMod ) )
3	2	simpld	|- ( F e. ( S NMHom T ) -> S e. NrmMod )